Skip to main content
SpringerLink
Log in

Frequency identification of Hammerstein-Wiener systems with backlash input nonlinearity

  • Regular Papers
  • Control Theory and Applications
  • Published:
International Journal of Control, Automation and Systems Aims and scope Submit manuscript

Abstract

The problem of system identification is addressed for Hammerstein-Wiener systems that involve memory operator of backlash type bordered by straight lines as input nonlinearity. The system identification of this model is investigated by using easily generated excitation signals. Moreover, the prior knowledge of the nonlinearity type, being backlash or backlash-inverse, is not required. The nonlinear dynamics and the unknown structure of the linear subsystem lead to a highly nonlinear identification problem. Presently, the output nonlinearity may be noninvertible and the linear subsystem may be nonparametric. Interestingly, the system nonlinearities are identified first using a piecewise constant signal. In turn, the linear subsystem is identified using a frequency approach.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. O. Nelles, Nonlinear System Identification, Springer, Berlin, 2001.

    Book  MATH  Google Scholar 

  2. J. Vörös, “An iterative method for Hammerstein-Wiener systems parameter identification,” Journal of Electrical Engineering, vol. 55, no. 11, pp. 328–331, 2004.

    Google Scholar 

  3. H. Li, Z. Chen, L. Wu, and H. Lam, “Event-triggered control for nonlinear systems under unreliable communication links,” IEEE Trans. Fuzzy Sys., vol. 25, no. 4, pp. 813–824, 2017.

    Article  Google Scholar 

  4. M. Wang, B. Chen, X. Liu, and P. Shi, “Adaptive fuzzy tracking control for a class of perturbed strict-feedback nonlinear time-delay systems,” Fuzzy Sets and Systems, vol. 159, no. 8, pp. 949–967, 2008. [click]

    Article  MathSciNet  MATH  Google Scholar 

  5. Q. Zhou, L. Wang, C. Wu, H. Li, and H. Du, “Adaptive fuzzy control for nonstrict-feedback systems with input saturation and output constraint,” IEEE Trans. Sys. Man and Cyb., 2016.

    Google Scholar 

  6. A. Nemati and M. Faieghi, “The performance comparison of ANFIS and Hammerstein-Wiener models for BLDC motors,” In: W. Hu (ed.), Electronics and Signal Processing. Lecture Notes In Electric Engineering, Springer, pp. 29–37, 2011. [click]

    Chapter  Google Scholar 

  7. H. C. Park, S. W. Sung, and J. Lee, “Modeling of Hammerstein-Wiener processes with special input test signals,” Ind. Eng. Chem. Res., vol. 45, no. 3, pp. 1029–1038, 2006.

    Article  Google Scholar 

  8. T. Patikirikorala, L. Wang, A. Colman, and J. Han, “Hammerstein-Wiener nonlinear model based predictive control for relative QoS performance and resource management of software systems,” Control Eng. Pract., vol. 20, no. 1, pp. 49–61, 2012.

    Article  Google Scholar 

  9. H. H. J. Bloemen, T. J. J. Boom, and H. B. Verbruggen, “Model-based predictive control for Hammerstein-Wiener systems,” Int. J. Control, vol. 74, no. 5, pp. 482–495, 2001. [click]

    Article  MathSciNet  MATH  Google Scholar 

  10. B. Ding and X. Ping, “Dynamic output feedback model predictive control for nonlinear systems represented by Hammerstein-Wiener model,” J. Process Control, vol. 22, no. 9, pp. 1773–1784, 2012. [click]

    Article  Google Scholar 

  11. M. Lawryńczuk, “Nonlinear predictive control for Hammerstein-Wiener systems,” ISA Transactions, vol. 55, pp. 49–62, 2015.

    Article  Google Scholar 

  12. C. K. Ahn, “l 2_ l ∞ elimination of overflow oscillations in 2-D digital filters described by Roesser model with external interference,” IEEE Trans. on Circ. & Sys. II, vol. 60, no. 6, pp. 361–365, 2013. [click]

    Google Scholar 

  13. C. K. Ahn, L. Wu, and P. Shi, “Stochastic stability analysis for 2-D Roesser systems with multiplicative noise,” Automatica, vol. 69, pp.356–363, 2016. [click]

    Article  MathSciNet  MATH  Google Scholar 

  14. C. K. Ahn and P. Shi, “Generalized dissipativity analysis of digital filters with finite wordlength arithmetic,” IEEE Trans. on Circ. & Sys. II, vol. 63, no. 4, pp. 386–390, 2016. [click]

    Google Scholar 

  15. C. K. Ahn and P. Shi, “Dissipativity analysis for fixed-point interfered digital filters,” Signal Processing, vol. 109, pp. 148–153, 2015. [click]

    Article  Google Scholar 

  16. J. Bruls, C. T. Chou, B. R. J. Heverkamp, and M. Verhaegen, “Linear and nonlinear system identification using separable least squares,” European J. Cont., vol. 5, no. 1, pp. 116–128, 1999.

    Article  MATH  Google Scholar 

  17. A. Wills and L. Ljung, “Wiener system identification using the maximum likelihood method,” Lith-Isy-R-2990, Springer, 2010.

    Google Scholar 

  18. A. Brouri, F. Giri, F. Ikhouane, F. Z. Chaoui, and O. Amdouri, “Identification of Hammerstein-Wiener systems with backlash input nonlinearity bordered by straight lines,” Proc. of 19th IFAC W.G., South Africa, August 24–29, pp. 475–480, 2014.

    Google Scholar 

  19. A. Brouri, O. Amdouri, F. Z. Chaoui, and F. Giri, “Frequency identification of Hammerstein-Wiener systems with piecewise affine input nonlinearity,” Proc. of 19th IFAC World Congress, South Africa, August 24–29, pp. 10030–10035, 2014.

    Google Scholar 

  20. M. Schoukens, E. W. Bai, and Y. Rolain, “Identification of Hammerstein-Wiener systems,” Proc. of 16th IFAC Symp. Syst. Identification, Belgium, pp. 274–279, 2012.

    Google Scholar 

  21. P. Crama and J. Schoukens, “Hammerstein-Wiener system estimator initialization,” Automatica, vol. 40, no. 9, pp. 1543–1550, 2004. [click]

    Article  MathSciNet  MATH  Google Scholar 

  22. E. W. Bai, “A blind approach to the Hammerstein-Wiener model identification,” Automatica, vol. 38, no. 6, pp. 967–979, 2002. [click]

    Article  MathSciNet  MATH  Google Scholar 

  23. R. Kalantari and M. S. Foomani, “Backlash nonlinearity modeling and adaptive controller design for an electromechanical power transmission system,” Transaction B: Mechanical Engineering, vol. 16, no. 6, pp. 463–469, 2009.

    MATH  Google Scholar 

  24. F. L. Lewis and R. R. Selmic, “Backlash compensation in nonlinear systems using dynamic inversion by neural networks,” Asian Journal of Control, vol. 2, no. 2, pp. 76–87, 2000.

    Google Scholar 

  25. B. Ni, M. Gilson, and H. Garnier, “Refined instrumental variable method for Hammerstein-Wiener continuous-time model identification,” IET Control Theory and Applic., vol. 7, no. 9, pp. 1276–1286, 2013.

    Article  MathSciNet  Google Scholar 

  26. M. Nordin and P. Gutman, “Controlling mechanical systems with backlash a survey,” Automatica, vol. 38, no. 10, pp. 1633–1649, 2002. [click]

    Article  MathSciNet  MATH  Google Scholar 

  27. R. Dong, Q. Tan, and Y. Tan, “Recursive identification algorithm for dynamic systems with output backlash and its convergence,” Int. J. Applied Math, Computer Science, vol. 19, no. 4, pp. 631–638, 2009. [click]

    Article  MathSciNet  MATH  Google Scholar 

  28. V. Cerone, D. Piga, and D. Regrunto, “Parameters bounds evaluation for linear systems with output backlash,” Proc. of IFAC Symposium on System Identification, France, pp. 575–580, 2009.

    Google Scholar 

  29. G. Tao and P. V. Kokotovic, Adaptive Control of Systems with Actuator and Sensor Nonlinearities, John Wiley & Sons, New York, 1996.

    MATH  Google Scholar 

  30. L. Ljung, System Identification, Theory For The User, Prentice Hall, NJ, USA, 1999.

    MATH  Google Scholar 

  31. D. Kozen and S. Landau, “Polynomial decomposition algorithms,” J. Symbolic Computation, vol. 7, no. 5, pp. 445–456, 1989. [click]

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. ENSAM- Meknes, AEEE Department, L2MC Laboratory, IMSM Team, Moulay Ismail University, Meknes, Morocco

    Adil Brouri

Authors
  1. Adil Brouri
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Laila Kadi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Smail Slassi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Adil Brouri.

Additional information

Recommended by Associate Editor Choon Ki Ahn under the direction of Editor Hyun-Seok Yang.

Adil Brouri In 2000, he obtained the Aggregation of Electrical Engineering and, in 2012, he obtained a Ph.D. in Automatic Control from the University of Mohammed 5, Morocco. He has been Professeur-Agrégé for several years. Since 2013 he joined the ENSAM (Higher National School of Arts and Trades), My Ismail University in Meknes-Morocco. He obtained his HDR degree in 2015 at the ENSAM-Meknes (My Ismail University). His research interests include nonlinear system identification and nonlinear control. He published several papers on these topics. Prof. Adil BROURI joined the research team “IMSM” (Multidisciplinary Engineering and Mechatronics Systems) and the L2MC (Mechanical, Mechatronics and Control) Laboratory as a permanent member.

Laila KADI he is currently completing his PhD in control of nonlinear systems under the supervision of Professor Adil Brouri, ENSAM, Moulay Ismail University.

Smail Slassi he is currently completing his PhD under the supervision of Professor Adil Brouri, ENSAM.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Brouri, A., Kadi, L. & Slassi, S. Frequency identification of Hammerstein-Wiener systems with backlash input nonlinearity. Int. J. Control Autom. Syst. 15, 2222–2232 (2017). https://doi.org/10.1007/s12555-016-0312-3

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12555-016-0312-3

Keywords

Search

Navigation